Hunting from either is certainly an option. There's lots things to consider. Do you intend to haul alot of gear, like big tents, full camp kitchen, a treestand, and the like? That would rule kayaks out. However, I don't think packing deer out with a kayak is out of the question. Arctic natives hunted seals and tied them to skin float bags to tow them back. If a deer wouldn't fit in a larger kayak, I don't doubt that it could still be towed this way if that was the only thing holding you back from a kayak.
A loose guideline to remember is that longer/narrower boats feel more "tippy" and don't turn as easily, but are easier and more efficient to paddle. Short and wide boats tend to be the opposite. So, do you plan on paddling small creeks and ponds or big open water? Will you be travelling upstream for any distance? Small waters lend themselves better to short, manueverable boats, while bigger waters or any significant upstream paddles will do better with something long and sleek. If you'll be on big open water, consider something "seaworthy" and that you are certain you can self rescue if you tip over. A sit-on-top kayak is the easiest to re-enter. Just climb back aboard. A canoe may be the most difficult to right, get back in, and bail out. In any case, make sure your boat has adequate flotation, with secured foam, sealed bulkheads, inflatable float bags, or a redundant combo thereof. (As a heads up, be aware that most of the recreational sit-in kayaks (especially the cheaper ones) have no sealed bulkheads, and need float bags to be safe if you're farther from shore than you can swim.)
Also, do you consider a boat simply a means to a hunting end, and/or with your only desire to have rudimentary paddling skills to get from A to B? Or do you want to learn advanced skills and get more performance out of a boat along the way? Just how "stable" of a boat are you looking for? How agile are you? Do you want room to move around or would you prefer to feel locked in?
Also, how are you going to carry a boat? Trailer, roof rack, truck bed? You're limited to short boats if you're planning on throwing them in the truck bed. Weight is a concern, too. Hefting a 65#+ boat on/off a roof rack and up/down to the launch site gets old fast after you've done it solo a few times. Also, where are you going to store a boat? Do you have room for anything long?
Your final decision may largely be like a longbow vs. recurve thing. In most cases, I think either would do the job, and the decision boils down to more of what you want from the boat while actually paddling it. I'm more of a kayak guy, favoring performance and ease of paddling. I paddle at least weekly and don't think I ever go out that I don't go at least a mile upriver, and often two. Sometimes three or four, and usually to hunt or fish. I personally don't find a kayak difficult to shoot out of, except straight down at fish. Here's my current favorite, an 18' x 22" wide Greenland kayak that I've even been paddling up small trout streams to fish.